10 citations · 43 across the 42 of their papers we have counts for
48 papers
Non-smooth sub-Riemannian manifolds with non-integer dimension and a Poincaré inequality
Sylvester Eriksson-Bique, Enrico Le Donne
For every integer and real number , we construct a -Ahlfors regular metric measure manifold of topological d…
Martingale and analytic dimensions
Sylvester Eriksson-Bique, Mathav Murugan
These notes introduce the martingale dimension of a strongly local regular Dirichlet form and the analytic dimension of a Lipschitz differentiability space. We explain why these di…
On universal elements for doubling geodesic trees
Sylvester Eriksson-Bique, Manisha Garg
For and , let denote the class of geodesic metric trees of valence at most whose branch points are uniformly relatively separated with c…
Embeddability and rectifiability of Lipschitz differentiability spaces
Ivan Caamano, Sylvester Eriksson-Bique, Elefterios Soultanis
We prove that Lipschitz differentiability spaces which bi-Lipschitz embed into an RNP-space are countably rectifiable. In contrast to earlier methods of Cheeger and Kleiner, our ap…
Quantitative non-embeddability theorems and metric embeddings of slit carpets
Sylvester Eriksson-Bique, Niilo Joutsenlahti
We study the bi-Lipschitz embedding problem for a class of metric spaces called slit carpets. First we show that the th stage of the standard slit carpet of Meren…
Cartesian products of Sierpiński carpets do not attain their conformal dimension
Riku Anttila, Sylvester Eriksson-Bique
It is a long-standing open question to determine whether the Sierpiński carpet attains its conformal dimension or not. While this problem remains unresolved, we prove that Cartesia…
On the Resistance Conjecture
Sylvester Eriksson-Bique
We give an affirmative answer to the resistance conjecture on characterization of parabolic Harnack inequalities in terms of volume doubling, upper capacity bounds and a Poincaré i…
Conformal dimension and its attainment on self-similar Laakso-type fractal spaces
Riku Anttila, Sylvester Eriksson-Bique, Lassi Rainio
A general construction of Laakso-type fractal spaces was recently introduced by the first two authors. In this paper, we establish a simple condition characterizing when the Ahlfor…
On the energy image density conjecture of Bouleau and Hirsch
Sylvester Eriksson-Bique, Mathav Murugan
We affirmatively resolve the energy image density conjecture of Bouleau and Hirsch (1986). Beyond the original framework of Dirichlet structures, we establish the energy image dens…
Quasisymmetric mappings on two variants of fractal percolation
Roope Anttila, Sylvester Eriksson-Bique, Aleksi Pyörälä
We study quasisymmetric maps on two variants of the classical fractal percolation model: the fat and dense fractal percolations. We show that, almost surely conditioned on non-exti…
Coarse and pointwise tangent fields
Guy C. David, Sylvester Eriksson-Bique, Raanan Schul
Alberti, Csörnyei and Preiss introduced a notion of a "pointwise (weak) tangent field" for a subset of Euclidean space -- a field that contains almost every tangent line of every c…
Uniqueness and nonuniqueness of -harmonic Green functions on weighted and metric spaces
Anders Björn, Jana Björn, Sylvester Eriksson-Bique +1
We study uniqueness of -harmonic Green functions in domains in a complete metric space equipped with a doubling measure supporting a -Poincaré inequality, with $1<p<\inft…
Construction of self-similar energy forms and singularity of Sobolev spaces on Laakso-type fractal spaces
Riku Anttila, Sylvester Eriksson-Bique, Ryosuke Shimizu
We construct self-similar -energy forms on a rich class of \emph{Laakso-type fractal spaces} and study the properties of the associated Sobolev spaces $\mathscr{…
Duality for the gradient of a -harmonic function and the existence of gradient curves
Sylvester Eriksson-Bique, Saara Sarsa
Every convex optimization problem has a dual problem. The -Dirichlet problem in metric measure spaces is an optimization problem whose solutions are -harmonic functions. What…
Self-improvement of fractional Hardy inequalities in metric measure spaces via hyperbolic fillings
Sylvester Eriksson-Bique, Josh Kline
In this paper, we prove a self-improvement result for -fractional Hardy inequalities, in both the exponent and the regularity parameter , for bounded dom…
Analytically one-dimensional planes and the Combinatorial Loewner Property
Guy C. David, Sylvester Eriksson-Bique
It is a major problem in analysis on metric spaces to understand when a metric space is quasisymmetric to a space with strong analytic structure, a so-called Loewner space. A conje…
The Combinatorial Loewner Property and super-multiplicativity inequalities for symmetric self-similar metric spaces
Riku Anttila, Sylvester Eriksson-Bique
This paper introduces a general construction of self-similar metric spaces as limits of discrete graphs. Our framework produces many classical examples, such as the Sierpiński carp…
On Constructions of Fractal Spaces Using Replacement and the Combinatorial Loewner Property
Riku Anttila, Sylvester Eriksson-Bique
The combinatorial Loewner property was introduced by Bourdon and Kleiner as a quasisymmetrically invariant substitute for the Loewner property for general fractals and boundaries o…
Universal Differentiability Sets in Laakso Space
Sylvester Eriksson-Bique, Andrea Pinamonti, Gareth Speight
We show that there exists a family of mutually singular doubling measures on Laakso space with respect to which real-valued Lipschitz functions are almost everywhere differentiable…
Fragment-wise differentiable structures
David Bate, Sylvester Eriksson-Bique, Elefterios Soultanis
The -modulus of curves, test plans, upper gradients, charts, differentials, approximations in energy and density of directions are all concepts associated to the theory of Sobol…
Sharp Hausdorff content estimates for accessible boundaries of domains in metric measure spaces of controlled geometry
Sylvester Eriksson-Bique, Ryan Gibara, Riikka Korte +1
We give a sharp Hausdorff content estimate for the size of the accessible boundary of any domain in a metric measure space of controlled geometry, i.e., a complete metric space equ…
Equality of different definitions of conformal dimension for quasiself-similar and CLP spaces
Sylvester Eriksson-Bique
We prove that for a quasiself-similar and arcwise connected compact metric space all three known versions of the conformal dimension coincide: the conformal Hausdorff dimension, co…
Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a -Poincaré inequality
Sylvester Eriksson-Bique, Ryan Gibara, Riikka Korte +1
We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "…
Density of continuous functions in Sobolev spaces with applications to capacity
Sylvester Eriksson-Bique, Pietro Poggi-Corradini
We show that capacity can be computed with locally Lipschitz functions in locally complete and separable metric spaces. Further, we show that if is a locally complete and…